Chapter 1
Randomized Controlled Trials
How best to understand and characterize causality is an age-old question in
philosophy. As such, one might expect that any discussion of causal inference
would need to be framed in terms of subtle and esoteric concepts. However,
a ground-breaking line of work starting with Neyman [1923] and Rubin [1974]
established that—although causality is in general a delicate and complicated
notion—there exists an important class of problems, randomized controlled
trials, where it is possible to approach causal questions in a practical and
conceptually straight-forward way via careful application of randomization,
averaging, and counterfactual reasoning.
1
This chapter presents a brief overview of statistical estimation and infer-
ence in randomized controlled trials (RCTs). When available, evidence drawn
from RCTs is often considered gold standard statistical evidence; and thus
methods for studying RCTs form the foundation of the statistical toolkit for
causal inference. Furthermore, many widely used observational study designs
in, e.g., econometrics or epidemiology are motivated by analogy to RCTs; and
so this chapter will also serve as a stepping stone to subsequent discussions of
estimation and inference in observational studies.
Average treatment effects Suppose that we have run a RCT with n study
participants i = 1, . . . , n, where each unit i is assigned a binary treatment
W
i
∈ {0, 1} and we then measure an outcome Y
i
. Our goal is to estimate the
effect of the treatment on the outcome. Following the Neyman–Rubin causal
model, we define the causal effect of a treatment via potential outcomes:
For each treatment level w ∈ {0, 1}, we define potential outcomes Y
i
(1) and
Y
i
(0) corresponding to the outcome the i-th subject would have experienced
had they respectively received the treatment or not, such that Y
i
= Y
i
(W
i
).
1
See Holland [1986] for one perspective on the work of Neyman [1923] and Rubin [1974]
in a historical context.
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